Three oligopolists operate in a market with inverse demand function given by()=where=1+2+3 and is the quantity produced by firm i. Each firm has constant marginal cost of production, c, and no fixed cost. The firms choose their quantities simultaneously.

1. Find the best response of each firm
2. Find the quantity each firm produces in the Nash equilibrium
3. Find the quantity each firm has to produce in order to maximize the joint
4. profits (assume that 1 = 2 = 3)
5. Explain why this is not an equilibrium